The present invention is related to the measurement and characterization of the flow effects and dynamic pressure impulse generated by an explosive airblast.
It is well known in the art that the initiation of an explosion at ground level will cause significant particle flow and dynamic pressure outward from the blast center. Several methods are currently in use to measure the magnitude of the blast, both in terms of velocity of the airflow and dynamic pressure at any given point radially outward from the blast center. One such method is to place numerous pressure transducers at given points along the blast path in order to measure the dynamic pressure at these points. This method is not only time consuming but very costly as a large quantity of transducers are necessary to properly characterize any given blast. A better method is to use displacement cubes to measure the effects of a blast. In this method, small cubes of material, generally metallic, and on the order of one cubic inch in volume, are placed along the blast path, and their displacement, after the blast, is measured. The dynamic pressure impulse of the blast can then be calculated according to the following equation: ##EQU1## Where: I=dynamic pressure impulse of the blast
m=mass of the displacement cube PA1 C.sub.d =coefficient of drag of the displacement cube PA1 V.sub.o =initial velocity of the displacement cube PA1 A=frontal area of the displacement cube PA1 t=time PA1 m=mass of the cube PA1 .mu.=resistance coefficient PA1 g=acceleration due to gravity PA1 V.sub.o =initial velocity
From the above equation it can be seen that to derive the dynamic pressure impulse of the blast from cube displacement, the initial velocity "V.sub.o " of the displacement cube must be determined. From experimental trials it was observed that a relationship exists between the initial velocity "V.sub.o " of the cube and the resulting displacement "D" of the cube. To verify that such a relationship exists, tests were conducted in which a metallic cube was launched over a hard-packed earth surface at different velocities and the displacements from the points of launch were measured. The cube was suspended about two inches above the surface on a fixture attached to the rear of a truck. The cube was held in this position until the truck was traveling at a selected speed, and then the cube was dropped. At speeds above 18 miles per hour, the speed of the truck was measured by a radar gun. Below 18 miles per hour, the speedometer of the truck was used.
Cube displacements were measured from the point of first contact with the ground to its final resting position. The orientation of the cube was uncontrolled after release, and could change somewhat during the two-inch fall, whereas cubes used in blast tests are initially on the ground with a face normal to the radial blast from ground zero. However, for displacements larger than around six feet, the effect of the differences in initial conditions is generally very small.
A mathematical model for the movement of a cube launched with an initial velocity "V.sub.o " can be constructed by assuming that the resistance to movement is a constant determined by the cube weight times a resistance coefficient, and results in the equation: ##EQU2## where x=displacement
For this model, the total displacement of the cube is given by the following equation: ##EQU3## where D=total displacement
This result indicates that if the model is adequate, the ratio D/V.sub.o.sup.2 should be constant, i.e. D/V.sub.o.sup.2 =C where "C" is a constant. Experimental data indicates that this is the case. Given this relationship, V.sub.o can now be expressed in terms of the constant "C" and cube displacement "D", thus, in the dynamic pressure impulse equation, V.sub.o can be replaced by the square root of D/C and the equation becomes: ##EQU4## where w=the weight of the cube.
From the above equation it can be seen that if "C" can be determined by calibration of the particular displacement cube to be used, determination of the dynamic pressure impulse "I" becomes a matter of routine calculation. The difficult part then is the calibration of the displacement cube. The present invention will overcome the drawbacks of the prior art method of displacement cube calibration. One significant drawback in the prior art was that accurate determination of the initial velocity "V.sub.o " of the cube was difficult. "V.sub.o " was first read in miles-per-hour from the vehicle's speedometer and then converted to feet-per-second, a cumbersome and error prone technique. A second drawback in the prior art method is the time required for each change in a velocity run. A third drawback in the prior art is the limited selection of surfaces over which the calibration can be done.